José R. Ortiz-Ubarri

Three-dimensional periodic optical orthogonal code for OCDMA systems

New families of three-dimensional (3-D) optical orthogonal codes for applications to optical code-division multiple access (OCDMA) networks are proposed. The families are based in the three dimensional periodic Welch Costas array over elementary Abelian groups. These new families are shown to be asymptotically optimal through the Johnson bound.

Enumeration of Costas Arrays Using GPUs and FPGAs

The enumeration of Costas arrays is a problem that grows factorially with input size and that has lately been completed for sizes up to 28 using computer clusters. This paper presents designs for solving this problem using, separately, GPUs and FPGAs. Both implementations rely on Costas array symmetries to reduce the search space and perform concurrent explorations over the remaining candidate solutions. The fine grained parallelism utilized to evaluate and progress the exploration, coupled with the additional concurrency provided by the multiple instanced cores allowed the FPGA (XC5VLX330-2) implementation to achieve speedups of up to 40 times over the GPU (GeForce GTX 480). Estimates for bigger sizes, up to N=28 indicate a speedup of 4.44 times over the fastest reported software implementation.

Double Periodic Arrays with Good Correlation for Applications in Watermarking

Digital watermarking applications require constructions of double-periodic matrices with good correlations. More specifically we need as many matrix sequences as possible with both good auto- and cross-correlation. Furthermore it is necessary to have double-periodic sequences with as many dots as possible. We have written this paper with the specific intention of providing a theoretical framework for constructions for digital watermarking applications. In this paper we present a method that increases the number of sequences, and another that increases the number of ones keeping the correlation good and double-periodic. Finally we combine both methods producing families of double-periodic arrays with good correlation and many dots. The method of increasing the number of sequences is due to Moreno, Omrani and Maric. The method to increase the number of dots was started by Nguyen, Lazlo and Massey, developed by Moreno, Zhang, Kumar and Zinoviev, and further developed by Tirkel and Hall. The very nice application to digital watermarking is due to Tirkel and Hall. Finally we obtain two new constructions of Optical Orthogonal Codes: Construction A which produces codes with parameters (n, ω, λ) = (p(p - 1), p2-1/2 , [p(p+1)/4]) and Construction B which produces families of code with parameters (n, ω, λ) = (p2(p-1), p2-1/2 , [p(p+1) 4]) and family size p + 1.

Group permutable constant weight codes

Improvements to the Johnson Bound for Optical Orthogonal Codes have been used to prove the optimality of double-periodic arrays with row and column length relatively prime. In our work we produce families of double-periodic arrays where the row and column length are not relatively prime. In this work we introduce the concept of group permutable constant weight codes and non-binary group permutable constant weight codes. We present improvements to the Johnson Bound to bound the cardinality of the families of double-periodic arrays whose row and column length are not relatively prime. We present some families of group permutable constant weight codes and prove the optimality of these families.

A new method to construct double periodic arrays with optimal correlation

Double-periodic arrays with good correlation are useful for applications in multiple target Costas and sonar, optical communications, and more recently digital watermarking. There are only a few double-periodic constructions with perfect correlation. In previous work we presented a method to construct families of double-periodic arrays with perfect correlation from the Welch Costas construction using the Chinese Remainder. In this work we introduce a similar method to construct new families of double-periodic arrays without using the Chinese Remainder. We apply this new method to the Quadratic sonar and the Welch Costas arrays to produce new families of double-periodic arrays with perfect correlation properties. We also apply the method to the family of quadratic sonars to produce new families of double-periodic arrays with close to perfect correlation. Finally we discuss the family size optimality of the constructions.

Algebraic Symmetries of Generic

In this paper, we present two generators for the group of symmetries of the generic (m+1) -dimensional periodic Costas arrays over elementary abelian (\BBZp)m groups: one that is defined by multiplication on m dimensions and the other by shear (addition) on m dimensions. Through exhaustive search, we observe that these two generators characterize the group of symmetries for the examples we were able to compute. Following the results, we conjecture that these generators characterize the group of symmetries of the generic (m+1) -dimensional periodic Costas arrays over elementary abelian (\BBZp)m groups.

(m+1)

Yang and Fuja [1] presented constructions of codes with unequal correlation constraints (λ<inf>c</inf> ≪ λ<inf>a</inf>). And specifically they have constructions for the case where λ<inf>a</inf> = 2 ≫ λ<inf>c</inf> = 1. In their work they argue that it is important to make the cross-correlation (λ<inf>c</inf>) as small as possible, and not necessarily λ<inf>a</inf> = λ<inf>c</inf>. In this work we present a method to generate new Yang-Fuja type families with correlation constraints where λ<inf>c</inf> ≪ λ<inf>a</inf>.

-Dimensional Periodic Costas Arrays

We present Toa, a web-based Network Flow data monitoring system (NMS). Toa consists of a collection of scripts that automatically parse network flow data, store this information in a database system, and generate interactive time line charts for network visualization analytics. The system is pseudo real time, meaning that it continuously updates the interactive charts from network flow data that is generated every five minutes. Toa also provides an interface to generate customized charts from the data stored in the database, and plugins that connect the visualization charts with the network flow data file for more in depth visualizations and analysis. The Toa web GUI presents users with the following network traffic visualization options: (1) per network label (interface, Autonomous System [AS], or network block) traffic, (2) per-port traffic for each network label, (3) network label to network label traffic, (4) customized charts from the database data, and (5) plugins for in-depth analysis of the network flow data file.

Constructions of families with unequal autoand cross-correlation constraints

We present q new asymptotically optimal families of doubly periodic arrays with ideal auto and cross correlation constraints, derived from the Moreno-Maric construction for frequency hopping applications. These new families possess the same properties that make the Moreno-Maric construction suitable for communications systems and digital watermarking, size (q+1)×(q+1), weight ω=q+1, family size q−2, and correlation 2, where q is a power of a prime. These new families are asymptotically optimal.